Double overflow hoses coming off the tank is a bit unusual. You only need one. Can you traces the two lines from the tank to where ever they may originate? I suspect one is the fill. Need to hand over hand trace the lines.
Can't explain why the water is going to the gray tank instead of the holding tank. I'm wondering if a past owner added a gray tank flush and rerouted the tank fill to the new tank flush. Know of a few campers that never fill their tank and only camp where they have city water available. If so I would disconnect. To great of a potential for cross contamination. Best to have an air gap between potable and waste systems.
Also the 'T' at the pump is probably the city water inlet to your fresh water system. Simplest place to add the 'T' plus ensures when winterizing an owner can remove as much water as possible starting at the source.
Good luck and post and update when you find the problem.
